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作者:Xiong Meng , Jennifer K. Ryan
来源:[J].Numerische Mathematik(IF 1.329), 2017, Vol.136 (1), pp.27-73
摘要:In this paper, an analysis of the accuracy-enhancement for the discontinuous Galerkin (DG) method applied to one-dimensional scalar nonlinear hyperbolic conservation laws is carried out. This requires analyzing the divided difference of the errors for the DG solution. We therefor...
作者:Balázs Kovács , Buyang Li , Christian Lubich ...
来源:[J].Numerische Mathematik(IF 1.329), 2017, Vol.137 (3), pp.643-689
摘要:For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the solution of the parabolic equation on ...
作者:Jiansong Zhang , Danping Yang , Hui Guo ...
来源:[J].Numerical Algorithms(IF 1.128), 2017, Vol.76 (4), pp.993-1019
摘要:Based on overlapping domain decomposition, we construct a parallel mixed finite element algorithm for solving the compressible miscible displacement problem in porous media. The algorithm is fully parallel. We consider the relation between the convergence rate and discretization ...
作者:Winfried Auzinger , Othmar Koch , Michael Quell
来源:[J].Numerical Algorithms(IF 1.128), 2017, Vol.75 (1), pp.261-283
摘要:We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several applications generating intricate pat...
作者:M. P. Rajan , G. D. Reddy
来源:[J].Mediterranean Journal of Mathematics(IF 0.641), 2017, Vol.14 (4)
摘要:In this paper, we consider a class of singularly perturbed elliptical problems with homogeneous boundary conditions. We consider a regularized iterative method for solving such problems. Convergence analysis and error estimate are derived. The regularization parameter is chosen a...
作者:Natalia Kopteva , Torsten Linß
来源:[J].Advances in Computational Mathematics(IF 1.468), 2017, Vol.43 (5), pp.999-1022
摘要:Linear and semilinear second-order parabolic equations are considered. For these equations, we give a posteriori error estimates in the maximum norm that improve upon recent results in the literature. In particular it is shown that logarithmic dependence on the time step siz...
作者:Xiaoli Li , Hongxing Rui
来源:[J].Journal of Scientific Computing(IF 1.71), 2017, Vol.72 (2), pp.863-891
摘要:In this article, a two-grid block-centered finite difference scheme is introduced and analyzed to solve the nonlinear time-fractional parabolic equation. This method is considered where the nonlinear problem is solved only on a coarse grid of size H and a linear problem is solved...
作者:Xiaofei Zhao
来源:[J].BIT Numerical Mathematics(IF 0.977), 2017, Vol.57 (3), pp.649-683
摘要:We apply the modulated Fourier expansion to a class of second order differential equations which consists of an oscillatory linear part and a nonoscillatory nonlinear part, with the total energy of the system possibly unbounded when the oscillation frequency grows. We comment on ...
作者:Changfeng Li , Yirang Yuan , Tongjun Sun ...
来源:[J].Journal of Scientific Computing(IF 1.71), 2017, Vol.72 (2), pp.467-499
摘要:A nonlinear system with boundary-initial value conditions of convection–diffusion partial differential equations is presented to describe incompressible nuclear waste disposal contamination in porous media. The flow pressure is determined by an elliptic equation, the concent...
作者:Chao Zhang , Dong-qin Gu , Zhong-qing Wang ...
来源:[J].Journal of Scientific Computing(IF 1.71), 2017, Vol.72 (2), pp.679-699
摘要:In this paper, we propose efficient space-time spectral methods for problems on unbounded domains. For this purpose, we first introduce two series of new basis functions on the half/whole line by matrix decomposition techniques. The new basis functions are mutually orthogonal in ...

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